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I found the main roads quite good -- well marked, well signed, etc. Some of the back roads, not so much. And as with almost anywhere, the locals can be overly aggressive -- coming up upon you WAY too fast, passing with barely enough clearance, and taking even blind corners on the wrong side of the road.... My advice: Just drive defensively, pull off when you can to let others pass, and enjoy your trip. Croatia can be lovely in mid-May.

Most of the drive is on the fast A1 toll road, a modern road (starts a ways north of Dubrovnik) better than some US interstate highways. Presumably you'll stop at Plitvice Lakes National Park before you get to Zagreb, so for that you'll get off the A1 onto the two land D1, which is slower of course but still a decent road.

You can pay tolls with credit cards at the A1 exits, FYI, at automated machines. You may need a chip card, not sure; I had a Visa with chip in it and used that last May a few times. I didn't need a PIN to use the card.

If you are driving between Dubrovnik and Split along the coast, note that you will pass through a small sliver of Bosnia called the Neum Corridor. So you will have to cross the border twice, once into and once out of Bosnia. If you have American passports, crossing should be quick and routine.

Check with your rental car company about crossing through the Neum corridor. Because technically you are leaving the EU(!) even if briefly, that may require some extra fee, but it is typical for tourists so they may give you a waiver - depends on the company's policies. If you are taking a ferry from Dubrovnik to an island or something, you might bypass these borders, however.

Otherwise, I found driving in Croatia very easy. Last May, there was very little traffic on the roads - tourist season had only barely begun.